Question

Given below are the analysis of variance results from a Minitab display. Assume you want to use a 0.05 significance level to test the null hypothesis that the 3 samples come from populations with the same mean. Based on these results, what can you conclude about the equality of the 3 population means? Briefly explain. Please show work, if any. Thank you in advance.

	DF	SS	MS	F	p
Factor	3	13.50	4.50	5.17	0.011
Error	16	13.925	0.870
Total	19	27.425

Answer 1

ANS

Hypothesis:  

H0: µ1 = µ2 = µ3

HA: µ1 ≠ µ2 ≠ µ3

where,

µ1, µ2, µ3 are the population means

Minitab Results

	DF	SS	MS	F	p
Factor	3	13.5	4.5	5.17	0.011
Error	16	13.925	0.87
Total	19	27.425

here,

P-Value (0.011) <0.05 (significance level) then we reject the H0

Conclusion:

We have sufficient evidence to conclude that 3 population mean are different or 3 samples not come from populations with the same mean.